Libel doesn't come into it unless a story is untrue.
However, the fact or otherwise of 'public interest' means very little to The Sun (or to be fair, most other tabloids). They conduct their 'journalism' by two maxims:
1. Will it sell lots of papers?
2. Is their own agenda fulfilled, and can they put their own self-interested spin on it?
In reality, they'll print anything which fulfills one or both of the above.
You're right, if you're sufficiently anonymous they'll have no interest in printing a story about you. But if you're in one of their 'target groups' MP's, 'celebs', anyone they don't like - the BBC, the police (since they fell out of love with them over the phone hacking), Labour politicians, etc, then watch out. They print plenty of stuff which isn't actually in the public interest, they just use that as a cover.
They set themselves up as Judge and Jury and tell you how to vote come election time, but when was the last time you ever heard of a journalist doing anything wrong unless exposed by other channels? Do these ring any bells...Phone hacking? Hillsborough? Elton John rent-boy slurs? Accusing the BBC of treason over Iraq when infact the BBC were quite right and The Sun were talking bollocks because they were cosied up to Blair? And do they ever give the right of reply if they fuck up, or even apologise? No.
And they don't want proper regulation because they bleat on about 'a free press' - that's patently bollocks, they just want the ability to print what they like to suit themselves, without any of the moral responsibility. TV News is regulated and they have plenty of worthy exposées, but they have to present a balanced view. The newspaper press don't want that, they want to ply their own blinkered and biased view.
By and large, they're vermin. Especially Murdoch's 'brand'.
Excellent post. That's why I never trust journos (I wonder how many journos are UKP members) and I trust them even less when the fuckers turn up here asking to interview punters about prositution/punting, etc. No matter what you say they will invariably add their spin to it.